Structure Theorem for Functionals in the Space 𠔖 ′ 𠜔 1, 𠜔 2

Hamed M. Obiedat, Wasfi A. Shatanawi and Mohd M. Yasein

International Journal of Mathematics and Mathematical Sciences, 2008, vol. 2008, 1-9

Abstract:

We introduce the space ð ”– 𠜔 1 , 𠜔 2 of all ð ¶ âˆž functions 𠜙 such that ð ‘ ð ‘¢ ð ‘ | ð ›¼ | ≤ ð ‘š ‖ ð ‘’ 𠑘 𠜔 1 𠜕 ð ›¼ 𠜙 ‖ ∞ and ð ‘ ð ‘¢ ð ‘ | ð ›¼ | ≤ ð ‘š ‖ ð ‘’ 𠑘 𠜔 2 𠜕 ð ›¼ 0 ð ‘¥ 0 0 0 5 ð ‘’ 𠜙 ‖ ∞ are finite for all 𠑘 ∈ â„• 0 , ð ›¼ ∈ â„• ð ‘› 0 , where 𠜔 1 and 𠜔 2 are two weights satisfying the classical Beurling conditions. Moreover, we give a topological characterization of the space ð ”– 𠜔 1 , 𠜔 2 without conditions on the derivatives. For functionals in the dual space ð ”– î…ž 𠜔 1 , 𠜔 2 , we prove a structure theorem by using the classical Riesz representation thoerem.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:756834

DOI: 10.1155/2008/756834

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